Coincidental Obscenity Deemed Extremely Dubious

Odds are California Gov. Arnold Schwarzenegger meant to deliver more than one message in a recent veto to the state Legislature, mathematicians say.

In the body of the message accompanying the veto, consisting of a four-line paragraph and a three-line paragraph, Mr. Schwarzenegger lamented that he was sent an "unnecessary" measure while "major issues are overlooked" in the cash-strapped state. But as the San Francisco Bay Guardian noted last week, the first letter of each of the seven lines spells out a profane rebuke that starts with "F" and ends with "you."

Unlikely Message

The governor's spokesman said the vertical vulgarity is a coincidence, which spurred mathematicians and statisticians to assess the probability that the coarse coded message could arise by chance. Their numbers were all over the map -- "We've had half a dozen reporters call with half a dozen different stats," Schwarzenegger spokesman Aaron McLear says -- but most statistics show that a coincidence was highly unlikely.

The first letter of each line in acrostic poems spells a word or phrase deliberately. But modern-day authors aren't always eager to own up to codes that are spotted. It doesn't take advanced cryptography to crack them, but common language patterns help assess how likely they are to emerge by chance.

And once a coded message is spotted, deniability isn't always plausible. Stephen Pollard, once an editorial writer at the U.K.'s Daily Express, pleaded coincidence. Just before he left the Express, an editorial he wrote formed an acrostic that began with the same message as the Schwarzenegger veto and was followed by "Desmond," the last name of the new Express owner, Richard Desmond.

Eight years later, Mr. Desmond has forgiven his former employee, who now writes occasionally for the Express. (Messrs. Desmond and Pollard didn't respond to requests for comment.) Similarly, California legislators shrugged off the Schwarzenegger veto message. Assemblyman Tom Ammiano, sponsor of the vetoed bill, called the message "pretty funny."

In an even more mathematically improbable case, a poem titled "The Leader" in an English-language textbook in Pakistan delivered an acrostic that spelled "President George W. Bush." The leader, the poem said, "tells it all straight, and means it all too." Pakistani officials weren't able to identify how the poem got into the textbook, but they deleted it from future editions because of criticism that the poem showed Pakistan was too supportive of the U.S.

Look hard enough for meaningful codes in a big enough collection of words, though, and you might find them. In the 1990s, researchers said they had discovered codes in the Bible. These codes spelled out names and seemingly forecast world events such as the assassination of Israeli Prime Minister Yitzhak Rabin. Some researchers were skeptical, showing that seemingly meaningful phrases also could be found in other, secular texts, such as "War and Peace."

Large texts such as the Bible are far more likely to contain aggressive statements than are brief missives. Brendan McKay, a computer scientist at Australian National University in Canberra, and one of the Bible-code skeptics, says that examining the King James translation of the Bible for coded messages with letters spaced at equal intervals in the code turns up such messages as "get lost," "go to hell," "you loser" and "I hate you."

"We shouldn't be too eager to claim a small 'probability' as a proof that something can't have happened accidentally," Prof. McKay wrote in an email.

Michael Drosnin, author of "The Bible Code," said critics of the code "have never produced any evidence that the codes are not real." Mr. Drosnin thinks the governor's veto message isn't like the Bible codes because it wasn't hidden. "This is an intentionally open message; you might say lit up in neon."

But Mr. Schwarzenegger claimed coincidence, which set the world of computational linguistics achatter. As a first effort to assess the governor's claim, several publications assumed that each letter in the English language is equally likely to be found at the beginning of a word. That means there was a 1-in-26 chance that the word opening the first line of the veto message started with an "F," and the same chance for each other line.

To calculate the chances that the seven letters would appear together in sequence, multiply 1/26 by itself seven times, which is 1 in 8.03 billion. That figure, based on an assumption that each letter is equally likely to appear, made headlines in the U.K.

Two mathematicians contacted by SF Weekly gave the governor the benefit of the doubt. They assumed that these letters were particularly common word openers, and assigned each a one-in-10 chance of appearing. That improves the probability that the governor's use of raw language was accidental to one in 10 million.

These calculations were intentionally set up to make the strongest possible case for coincidence. But in reality, says Stephen Devlin, a mathematician at the University of San Francisco, coincidence "is very, very, very unlikely."

To quantify just how unlikely, researchers needed to know how frequently each letter in the message begins English-language words. They turned to corpora, large collections of text, to calculate the frequency with which, say, words starting with "U" appear in the language.

Steven Piantadosi, a graduate student in cognitive sciences at the Massachusetts Institute of Technology, used a collection of texts, many of them from the U.K., comprising 17.9 million words. By analyzing the typical frequency of letters in the English language, he calculated the odds of such a salty lineup of letters appearing accidentally at slightly less than one in one trillion. Other studies yielded similar odds.

It is possible that Mr. Schwarzenegger is more prone to use words that begin with the letters that made up the coded message. For instance, "K" is the fourth-least-likely letter to start a word, according to Mr. Piantadosi. But the "K" in the veto message comes from a statement that the state Legislature "kicks the can down the alley." Mr. McLear says the governor has been using that phrase for years.

Other words have appeared acrostic-style in the left margin of some messages accompanying about 1,700 Schwarzenegger vetoes. Mr. McLear points to examples such as "ear," "poet" and "soap." But mathematicians note that three- or four-letter words with more common letters are far more likely. "The odds of an identifiably obnoxious line is small," Gregory McColm, a mathematician at the University of South Florida, wrote in an email.

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